Search: id:A001918
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%I A001918 M0242 N0083
%S A001918 1,2,2,3,2,2,3,2,5,2,3,2,6,3,5,2,2,2,2,7,5,3,2,3,5,2,5,2,6,3,3,2,3,2,2,
               6,
%T A001918 5,2,5,2,2,2,19,5,2,3,2,3,2,6,3,7,7,6,3,5,2,6,5,3,3,2,5,17,10,2,3,10,2,
               2,
%U A001918 3,7,6,2,2,5,2,5,3,21,2,2,7,5,15,2,3,13,2,3,2,13,3,2,7,5,2,3,2,2,2,2,2,
               3
%N A001918 Least positive primitive root of n-th prime.
%D A001918 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 864.
%D A001918 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 
               1976, page 213.
%D A001918 CRC Handbook of Combinatorial Designs, 1996, p. 615.
%D A001918 P. Fan and M. Darnell, Sequence Design for Communications Applications, 
               Wiley, NY, 1996, Table A.1.
%D A001918 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               5th ed., Oxford Univ. Press, 1979, th. 111
%D A001918 Hua Loo Keng, Introduction To Number Theory, 'Table of least primitive 
               roots for primes less than 50000', pp. 52-6, Springer NY 1982.
%D A001918 R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, 
               Univ. Texas Press, 1961.
%D A001918 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001918 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001918 N. J. A. Sloane, <a href="b001918.txt">Table of n, a(n) for n = 1..10000</
               a>
%H A001918 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A001918 Anonymous, <a href="http://www.gotmath.com/primroot.txt">Primes less 
               than 10000 and their smallest primitive roots</a>
%H A001918 K. Matthews, <a href="http://www.numbertheory.org/php/lprimroot.html">
               Finding the least primitive root (mod p), p an odd prime</a>
%H A001918 T. Oliveira e Silva, <a href="http://www.ieeta.pt/~tos/p-roots.html">
               Least primitive root of prime numbers</a>
%H A001918 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimitiveRoot.html">Link to a section of The World of Mathematics.</
               a>
%e A001918 modulo 7: 3^6=1, 3^2=2, 3^7=3, 3^4=4, 3^5=5, 3^3=6, 7=p(4), 3=a(4)
%p A001918 with(numtheory); A001918 := primroot;
%t A001918 (* first do *) Needs["NumberTheory`NumberTheoryFunctions`"] (* then *) 
               Table[ PrimitiveRoot@Prime@n, {n, 101}] (from Robert G. Wilson v 
               (rgwv(at)rgwv.com), Dec 15 2005)
%o A001918 (PARI) for(x=1,1000,print(lift(znprimroot(prime(x)))))
%o A001918 (Other) sage: print [primitive_root(p) for p in primes(570)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), May 24 2009]
%Y A001918 A column of A060749. Cf. A002233.
%Y A001918 Sequence in context: A127808 A127809 A127810 this_sequence A002233 A159953 
               A074595
%Y A001918 Adjacent sequences: A001915 A001916 A001917 this_sequence A001919 A001920 
               A001921
%K A001918 nonn,nice,easy
%O A001918 1,2
%A A001918 N. J. A. Sloane (njas(AT)research.att.com).

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